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DESIGNERS' CHARTS 
FOR REINFORCED CONCRETE 




JOINT COMMITTEE STANDARDS 




Book t 






Copyright N°_ 



COPYRIGHT DEPOSre 



II 



THE DESIGN OF 5/#-v> 

REINFORCED CONCRETE SLABS 

BEAMS AND COLUMNS 



CONFORMING TO THE RECOMMENDATIONS OF THE 

JOINT COMMITTEE ON CONCRETE AND REINFORCED CONCRETE 

COMPOSED OF COMMITTEES OF THE 

American Society of Civil Engineers American Society for Testing- Materials 

American Railway Engineering- and Maintenance of Way Association 

Association of American Portland Cement Maniifactnrers 



By H. B. ANDREWS, JMem. Am. Soc. C. E. 

DESIGNIXG ESTGINEEE, SIMPSON BROS., Cobpobation 
AUTHOR AND PUBLISHER 

166 DEVONSHIRE STREET, BOSTON, MASS. 

1909 



PRICE, ^1.00 



COPYRIGHT, 1009, BY H. B. ANDREWS, BOSTON, MASS. 



©01A25S261 



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PREFACE 

The need of standard methods for designing reinforced concrete has long been felt, 
as there has been heretofore little unity in practice. 

It is the purpose of this pamphlet with its accompanying charts to present standard 
reinforced concrete sections based on the most authentic data, in a simple form, so that 
any designer, whether entirely conversant with reinforced concrete or not, will not go astray 
in his calculations. 

From 1899 to 1904 committees from the societies named on the title page were ap- 
pointed to study the subject of concrete and reinforced concrete. In June, 1904, these 
several committees consohdated, and since that time have been preparing a report on the 
subject. This report of the joint committee was presented at the January, 1909, meeting 
of the American Society of Civil Engiaeers and ordered pubUshed in their proceedings. 
The Joint Committee was composed of thirty members and the report was signed by twenty- 
four of the thirty. It is thus the most authoritative treatise on concrete presented to the 
public, and therefore warrants its careful consideration. 

The texts and charts herein conform as closely as possible to the recommendations 
embodied in the report of the Joint Committee and the calculations have been verified by 
Sanford E. Thompson, Member American Society of Civil Engineers, a member of the 
committee, to whose valued assistance the author is very much indebted. 

H. B. ANDREWS. 



GENERAL RECOMMENDATIONS* 

Rules for structures of reinforced concrete for the purpose of fixing the responsibility and 

providing for adequate supervision during construction 



a. Before work is commenced, complete plans 
should be prepared, accompanied by specifications, 
static computations and descriptions showing the general 
arrangement in all details. The static computations 
shall give loads assumed separately, such as dead and 
live loads, wind and impact, if any, and the resulting 
stresses. 

6. The specifications shall state the qualities of the 
materials to be used for making the concrete, and the 
proportions in which the}^ are to be mixed. 

c. The strength which the concrete is expected to 
obtain after a definite period shall be stated in the speci- 
fications. 

d. The drawings and specifications shall be signed by 
the engineer and contractor. 

e. The approval of the plans and specifications by 
the other authorities shall not relieve the engineer nor 
the contractor of responsibility. 

/. Inspection during construction shall be made by 
competent inspectors employed by, and under the 
supervision of the engineer, and shall cover the following : 



1. 
2. 



4. 



6. 



The materials. 

The correct construction and erection of the 
forms and supports. 

The sizes, shapes and arrangement of the rein- 
forcement. 

The proportioning, mixing and placing of the 
concrete. 

The strength of the concrete by tests of standard 
test pieces made on the work. 

Whether the concrete is sufficiently hardened 
before the forms and supports are removed. 



7. Prevention of injury to any part of the structure 

by and after the removal of the forms. 

8. Comparison of dimensions of all parts of the 

finished structure with the plans. 

g. Load tests on portions of the finished structure 
shaU be made where there is reasonable suspicion that 
the work has not been properly performed, or that, 
through influences of some kind, the strength has been 
impaired. Loading shall be carried to such a point that 
twice the calculated working stresses in critical parts are 
reached, and such loads shall cause no permanent defor- 
mations. Load tests shall not be made until after sixty 
days of hardening. 

Materials 

Cement. — The cement shall meet the requirements of the 
standard specifications for cement adopted August 15, 
1908, by the American Society for Testing Materials. 

A^^re^ate. — Extreme care should be exercised in selecting 
the aggregates for mortar and concrete, and careful tests 
made of the materials for the purpose of determining 
their qualities and the grading necessary to secure maxi- 
mum density or a minimum percentage of voids. 

Fine A^^re^ate. — a. Fine aggregate consists of sand, 
crushed stone or gravel screenings, passing, when dry, a 
screen having one quarter inch diameter holes. 

It should be preferably of siliceous material, clean, 
coarse, free from vegetable loam or other deleterious 
matter, and not more than six per cent should pass a 
sieve having one hundred meshes per linear inch. 



*Quoted direct from Joint Committee Report. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[4 



A gradation of the grain from fine to coarse is gen- 
erally advantageous. 

Mortars composed of one part Portland cement and 
three parts fine aggregate by weight when made into 
briquets should show a tensile strength of at least seventy 
per cent of the strength of 1 :3 mortar of the same con- 
sistency made with the same cement and standard 
Ottawa sand. 

Coarse A^^re^ate. — h. Coarse aggregate consists of inert 
material, such as crushed stone or gravel, which is re- 
tained on a screen having one quarter inch diameter 
holes. The particles should be clean, hard, dm*able, and 
free from all deleterious materials. Aggregates contain- 
ing soft, flat or elongated particles should be excluded 
from important structures. 

A gradation of sizes of the particles is generally 
advantageous. 

The maximum size of the coarse aggregate shall be 
such that it will not separate from the mortar in laying 
and will not prevent the concrete fully surrounding the 
reinforcement or filling all parts of the forms. 

Where concrete is used in mass the size of the 
coarse aggregate may be such as to pass a three-inch 
ring. For reinforced members a size to pass a one-inch 
ring is a customary maximum. 

Cinder Concrete. — Cinder concrete is not suitable for re- 
inforced concrete structures, and may be safely used 
only in mass for very light loads or for fire-proofing. 
Where ciader concrete is permissible, the cinders used 
as the coarse aggregate should be composed of hard, 
clean, vitreous clinker, free from sulphides, unburned 
coal or ashes. 

Water. — The water used in mixing concrete should be free 
from oil, acid, strong alkalies or vegetable matter. 

Metal Reinforcement. — The committee recommends as a 
suitable material for reinforcement steel filling the require- 
ments of the specifications adopted by the American Rail- 
way Engineering and Maintenance of Way Association. 



For the reinforcement of slabs, smaU beams, or 
minor details, or for the prevention of shrinkage cracks, 
or where wire or small rods are suitable, material con- 
forming to the requirements of either specification "A" 
or "B" may be used. 

The reinforcement should be free from rust, scale, 
or coatings of any character which would tend to reduce 
or destroy the bond. 

Preparation and Placing of Mortar 
and Concrete 

Proportions. — The material to be used in concrete should 
be carefully selected, of uniform quality, and propor- 
tioned with a view of securing as nearly as possible a 
maximum density. 

Unit of Measure. — a. The unit of measure should be the 
barrel, which should be taken as containing 3.8 cubic feet. 
Four bags containing ninety-four pounds of cement each 
should be considered the equivalent of one barrel. 

Fine and coarse aggregate should be measured 
separately as loosely thrown in to the measuring recep- 
tacle. 

Relation of Fine and Coarse A^^re^ate. — b. The fine 
and coarse aggregate should be used in such relative pro- 
portions as wiU insure maximum density. In unim- 
portant work it is sufficient to do this by individual 
judgment, using correspondingly higher proportions of 
cement; for important work these proportions should be 
carefully determined by density experiments and the siz- 
ing of the fine and coarse aggregates maintained uniform 
or the proportions changed to meet the varjdng sizes. 

Relation of Cement and A^^re^ate. — c. For reinforced 
concrete construction a density proportion based on 1 :6 
should generally be used, i.e., one part of cement to a 
total of six parts of fine and coarse aggregates measured 
separately. In columns richer mixtures are often re- 
quired, while for massive masonry or rubble concrete a 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[5 



leaner mixture of 1 :9 or even 1 :12 may be used. These 
proportions should be determined by the strength or 
wearing qualities required in the construction at the 
critical period of its use. Experienced Judgment based 
on individual observation and tests of similar conditions 
in similar localities is the best guide as to the proper 
proportions for any particular case. 

Mixing. — The ingredients of concrete should be thoroughly 
mixed to the desired consistency and the mixing should 
continue until the cement is uniformly distributed and 
the mass is uniform in color and homogeneous, since 
maximum density and therefore greatest strength of a 
given mixture depends largely on thorough and complete 
mixing. 

Measuring Proportions. — a. Methods of measurement 
of the proportions of the various ingredients, including 
the water, should be used, which will secure separate 
uniform measurements at all times. 

Machine Mixing. — h. When the conditions will permit, 
a machine mixer of a type which insures the proper 
proportioning of the materials throughout the mass 
should be used, since a more thorough and uniform 
consistency can be thus obtained. 

Hand Mixing. — c. When it is necessary to mix by hand, 
the mixing should be on a water-tight platform and 
especial precautions should be taken to turn the materials 
until they are homogeneous in appearance and color. 

Consistency. — d. The materials should be mixed wet 
enough to produce a concrete of such a consistency as 
will flow into the forms and about the metal reinforce- 
ment, and which, on the other hand, can be conveyed 
from the mixer to the forms without separation of the 
coarse aggregate from the mortar. 

Retemperind. — e. Retempering mortar or concrete, i.e., 
remixing with water after it has partially set, should not 
be permitted. 



Placing of Concrete 

Methods. — a. Concrete, after the addition of water to 
the mix, should be handled rapidly, and in as small 
masses as is practicable, from a place of mixing to the 
place of final deposit, and under no circumstances should 
concrete be used that has partially set before final placing. 
A slow setting cement should be used when a long time 
is liable to occur between mixing and final placing. 

The concrete should be deposited in such a manner 
as wiU permit the most thorough compacting, such as 
can be obtained by working with a straight shovel or 
slicing tool kept moving up and down until all the 
ingredients have settled in their proper place by gravity 
and the surplus water forced to the surface. 

In depositing the concrete under water, special care 
should be exercised to prevent the cement from being 
floated away, and to prevent the formation of laitance, 
which hardens very slowly and forms a poor surface on 
which to deposit fresh concrete. Laitance is formed in 
both still and running water, and should be removed 
before placing fresh concrete. 

Before placing the concrete care should be taken to 
see that the forms are substantial and thoroughly wetted 
and the space to be occupied by the concrete free from 
debris. When the placing of the concrete is suspended, 
all necessary grooves for joining future work should be 
made before the concrete has had time to set. 

When work is resumed, concrete previously placed 
should be roughened, thoroughly cleansed from foreign 
material and laitance, drenched and slushed with a 
mortar consisting of one part Portland cement and not 
more than two parts fine aggregate. The faces of con- 
crete exposed to premature drying should be kept wet 
for a period of at least seven days. 

Freezing Weather. — h. The concrete for reinforced struc- 
tures should not be mixed or deposited at a freezing tem- 
perature, unless special precautions are taken to avoid 
the use of materials containing frost or covered with ice 
crystals, and providing means to prevent the concrete 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[6 



from freezing after being placed in position and until it 
has thoroughly hardened. 

Rubble Concrete. — c. Where the concrete is to be depos- 
ited in massive work, its value may be improved and its 
cost materially reduced through the use of clean stones 
thoroughly imbedded in the concrete as near together 
as is possible and still entirely surrounded by concrete. 

Forms 

Forms should be substantial and un5delduig, so that 
the concrete shall conform to the designed dimensions 
and contours, and should be tight, to prevent the leakage 
of mortar. 

The time for removal of forms is one of the most 
important steps in the erection of a structure of concrete 
or reinforced concrete. 

Care should be taken to inspect the concrete and 
ascertain its hardness before removing the forms. 

So many conditions affect the hardening of concrete, 
that the proper time for the removal of forms should be 
decided by some competent and responsible person, 
especially where the atmospheric conditions are im- 
favorable. 

Details of Construction 

Joints; Reinforcement. — Wherever in tension reinforce- 
ment it is necessary to splice the reinforcing bars, the 
length of lap shall be determined on the basis of the safe 
bond stress and the stress in the bar at the point of 
spUce; or a connection shall be made between the bars 
of sufficient strength to carry the stress. Splices at 
points of maximum stress should be avoided. In columns 
large bars should be butted and sphced; small bars may 
be treated as indicated for tension reinforcement or their 
stress may be taken off by being imbedded in large 
masses of concrete. At foundations, bearing plates 
should be provided for large bars or structural forms. 



Concrete. — For concrete construction it is desirable to cast 
the entire structure at one operation, but as this is not 
always possible, especially in large structures, it is neces- 
sary to stop the work at some convenient point. This point 
should be selected so that the resulting joint may have 
the least possible effect on the strength of the structure. 

It is therefore recommended that the joint in columns 
be made flush with the lower side of the girders; that the 
joints in girders be at a point midway between supports, 
but should a beam intersect a girder at this point, the 
joint should be offset a distance equal to twice the width 
of the beam; that the joints in the members of a floor 
system should in general be made at or near the center 
of the span. 

Joints in columns should be perpendicular to the 
axis of the column, and in girders, beams and floor slabs 
perpendicular to the plane of their surfaces. 

Shrinkage. — Girders should never be constructed over freshly 
formed columns without permitting a period of at least 
two hours to elapse, thus providing for settlement or 
shrinkage in the columns. Before resuming work, the 
top of the column should be thoroughly cleansed of 
foreign matter and laitance. If the concrete in the 
column has become hard the top should also be drenched 
and slushed with a mortar consisting of one part Portland 
cement and not more than two parts fine aggregate before 
placing additional concrete. 

Temperature Changes. — Concrete is sensitive to tem- 
perature changes and it is necessary to take this fact into 
account in designing and erecting concrete structures. 
In some positions the concrete is subjected to a much 
greater fluctuation in temperature than in others, and in 
such cases joints are necessary. The frequency of these 
joints will depend, first, upon the range of temperature 
to which the concrete wiU be subjected; second, upon the 
quantity and position of the reinforcement. 

These points should be determined and provided 
for in the design. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[7 



In massive work, such as retaining walls, abutments, 
etc., built without reinforcement, joints should be pro- 
vided, approximately, every fifty feet throughout the 
length of the structure. To provide against the struc- 
tures being thrown out of line by unequal settlement, each 
section of the wall may be tongued and grooved into the 
adjoining section. 

To provide against unsightly cracks, due to unequal 
settlement, a joint should be made at all sharp angles. 

Fire-proofing. — It is recommended that in monolithic 
concrete columns, the concrete to a depth of one and one 
half inches be considered as protective covering and not 
included in the effective section. 

For ordinary conditions it is reconunended that the 
metal in girders and columns be protected by a minimum 
of two inches of concrete; that the metal in beams be 
protected by a minimum of one and one half inches of 
concrete, and that the metal in floor slabs be protected 
by a minimum of one inch of concrete. 

It is recommended that the corners of columns, 
girders and beams be beveled or rounded, as a sharp 
corner is more seriously affected by fire than a round one. 



General Assumptions for Loads 

Loads. — The loads or forces to be resisted consist of: — 
1 . The dead load, which includes the weight of 
the structure and fixed loads and forces. 

2 . The live load, or the loads and forces which are 
variable. The d3mamic effect of the five load will often 
require consideration. Any allowance for the dynamic 
effect is preferably taken into account by adding the 
desired amount to the live load or to the live load stresses. 
The working stresses hereinafter recommended are 
intended to apply to the equivalent static stresses so 
determined. 

In the case of high buildings the five load on columns 
may be reduced in accordance with the usual practice. 



Reinforced Concrete Slabs 

Span. — The span length for slabs shall be taken as the 
distance from center to center of supports, but shaU not 
exceed the clear span plus the depth of slab. 

Reinforcement. — Floor slabs shaU be designed and rein- 
forced as continuous over intermediate supports. The 
chart takes into consideration reinforcement in one 
direction only. Reinforcement shaU be fuUy provided at 
points of negative moment. 

In computing the positive and negative moments 
in slabs continuous over several supports due to uniformly 
distributed loads, the following rules are given : — 

1. That for floor slabs, the bending moment at 
center and at support be taken at wP^12 for both dead 
and live loads where w represents the load per linear 
foot and 1 the span length. 

2. That for floor slabs over one or two bays only, 
the bending moment shaU be taken at wP-^10 for both 
dead and live loads. 

3. Special consideration is required in the case of 
concentrated loads. 

4. Reinforcement is to be lapped a suflacient dis- 
tance over supports to provide adequate bond strength. 

5. The center of slab reinforcement shall be one 
inch above bottom of slab at middle of span, and one 
inch from top of slab over supports. 

Working Stresses. — The extreme fiber stress of a slab may be allowed to 
reach 650 pounds per square inch for 1:2:4 concrete, conforming to Joint 
Committee requirements, under assumed working loads. 

The tensile strength in steel may be allowed to reach 16,000 pounds 
per square inch under assumed working loads. 



Reinforced Concrete Beams 

Span. — The span length for beams shall be taken as the dis- 
tance from center to center of supports, but shall not be 
taken to exceed the clear span plus the depth of beam. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[8 



T- Beams. — In beam and slab construction an effective 
bond shall be provided at the junction of beam and slab. 
When the principal slab reinforcement is parallel to the 
beam, transverse reinforcement shall be used extending 
over the beam and well into the slab. 

Where adequate bond between the slab and web of 
beam is provided, the slab may be considered as an 
integral part of the beam, but its effective width shall 
be determined by the following rules : — 

a. It shah not exceed one fourth of the span length 
of the beam; 

6. Its overhanging width on either side of the web 
shaU not exceed four times the thickness of the slab. 

(Note. — WTiere the width of slab does not equal 
the effective width allowed by these rules, special con- 
sideration must be given to make assurance that the 
concrete in slab is not overstressed in compression.) 

c. In the designs of T-beams acting as continuous 
beams, due consideration shaU be given to the com- 
pressive stresses at the supports. 

Reinforcement. — Beams shall be designed and reinforced 
as continuous over intermediate supports. Reinforcement 
shall be fuUy provided at points of negative moment. 

In computing the positive and negative moments, in 
beams and slabs continuous over several supports, due to 
uniformly distributed loads, the following rule is given: — 

That for beams the bending moment at center and 
at supports for interior spans be taken at wP -^12, and 
for end spans it be taken as wP -^ 10 for center and ad- 
joining support for dead and live loads. 

In the case of beams continuous for two spans only, 
more exact calculations should be made. Special con- 
sideration is also required in the case of concentrated loads. 

Where beams are reinforced on the compressive side, 
the steel may be assumed to carry its proportion of the 
stress. 

In the case of continuous beams, tensile and com- 
pressive reinforcement must extend sufficiently beyond 
the support to develop the requisite bond stress. 



Bond Strength and Spacing of Bars. — Adequate bond 
strength should be provided in accordance with the 
formula hereinafter given. Where a portion of the bars 
is bent up near the end of a beam, the bond stress in the 
remaining straight bars will be less than is represented 
by the theoretical formula. 

Where high bond resistance is required, the deformed 
bar is a suitable means of supplying the necessary 
strength. Adequate bond strength throughout the length 
of a bar is preferable to end anchorage, but such anchor- 
age may be properly used in special cases. Anchorage 
furnished by short bends at a right angle is less effective 
than hooks consisting of turns through 180 degrees. 

The lateral spacing of parallel bars should not be 
less than two and one haK diameters, center to center, 
nor should the distance from the side of the beam to the 
center of the nearest bar be less than two diameters. 

The clear spacing between two layers of bars should 
not be less than one half inch. 



Shear and Diagonal Tension. — Calculations for web re- 
sistance shall be made on the basis of maximum shearing 
stress, as determined by the formulas hereinafter given. 
When the maximum shearing stresses exceed the value 
allowed for the concrete alone, web reinforcement must 
be provided to carry the diagonal tension stresses. This 
web reinforcement may consist of bent bars, or inclined 
or vertical members attached to or looped about the 
horizontal reurforcement. Where inclined members are 
used, the connection to the horizontal reinforcement 
shall be such as to insure against shp. 

The followuig allowable values for the maximum 
shearing stress are recommended : — 

a. For beams with horizontal bars only 40 pounds 
per square inch. 

&. For beams in which a part of the horizontal rein- 
forcement is used in the form of bent-up bars, arranged 
with due respect to the shearing stresses, a higher value 
may be allowed, but not exceed 60 pounds per square inch. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[9 



c. For beams thoroughly reinforced for shear a 
value not exceeding 120 pounds per square inch. 

In the calculation of web reinforcement to provide 
the strength required under c above, the concrete may 
be counted upon as carrying one thnd of the shear. 
The remainder is to be provided for by means of metal 
reinforcement, consisting of bent bars or stirrups, but 
preferabty both. The requisite amount of such rein- 
forcement maybe estimated on the assumption that the 
entire shear on a section, less the amount assumed to be 
carried by the concrete, is carried by the reinforcement 
in a length of beam equal to its depth. 

The longitudinal spacing of stirrups or bent rods 
shall not exceed three fourths the depth of the beam. 

It is important that adequate bond strength be 
provided to fully develop the assumed strength of aU 
shear reinforcement. 

Inasmuch as small deformations in the horizontal 
reinforcement tend to prevent the formation of diagonal 
cracks, a beam will be strengthened against diagonal 
tension failure by so arranging the horizontal reinforce- 
ment that the unit stresses at points of large shear shall 
be relatively low. 

Working Stresses. — The extreme fiber stress of a beam may be allowed to 
reach 650 pounds per square inch for 1:2:4 concrete conforming to Joint 
Committee requirements, under assumed working loads. Adjacent to 
the support of continuous beams 750 pounds per square inch may be used. 
The tensile stress in steel may be allowed to reach 16,000 pounds per 
square inch, and the compressive stress in steel at supports 11,250 pounds 
per square inch in 1 : 2: 4 concrete. 

For working stresses for bond, shear and diagonal tension see page 10. 

Columns 

Length. — The ratio of unsupported length to the least 
width of any column shall be limited to 10. 

Effective Area. — This shall be taken as the area within 
the protective covering. Or in the case of hooped col- 



umns or columns reinforced with structural shapes, it 
shall be taken as the area Avithin the hooping or struc- 
tural shapes. 

Reinforcement. — Columns may be reinforced with longi- 
tudinal bars by bands or hoops together with longitudinal 
bars, or by means of structural forms which in them- 
selves are sufficiently rigid to act as columns. 

Bars composing longitudinal reinforcement shall be 
straight, and shall have sufficient lateral support to be 
securely held in place until the concrete is set. 

AVhere bands or hoops are used, the total amount of 
such reinforcement shall be not less than one per cent 
of the volume of concrete enclosed. 

The clear spacing of such bands or hoops shall be 
not greater than one fourth the diameter of the enclosed 
column. Adequate means must be provided to hold the 
bands or hoops in place so as to form a column, the core 
of which shall be straight and well centered. 

Bending stresses due to eccentric loads must be pro- 
vided for by increasing the section until the maximum 
stress does not exceed the value above specified. 

Working Stresses. — 1- For plain concrete columns, or for columns with . 
longitudinal reinforcement only, 450 pounds per square inch for 1:2:4 
concrete, and 562.5 pounds per square inch for 1:1^:3 concrete, con- 
forming to Joint Committee requirements. (Described as "A" on chart.) 

2. For columns reinforced with bands or hoops, 540 pounds per 
square inch for 1:2:4 concrete, and 675 pounds per square inch for 
1:1J:3 concrete. (Described as "B" on chart.) 

3. For columns reinforced with not less than 1 per cent and not 
more than 4 per cent of longitudinal bars and with bands or hoops, 640 
pounds per square inch for 1:2:4 concrete and 800 pounds per square 
inch for 1 : IJ: 3 concrete. (Described as "C" on chart.) 

4. For columns reinforced with structural steel column units which 
thoroughly encase the concrete core, the same stresses as given for 3. 

5. For longitudinal reinforcement, not less than 1 per cent, and not 
over 4 per cent of the effective area of the concrete, 15 times the unit 
stress allowed in the concrete may be used. 

Fire-proofing. — Concrete to the depth of 1| inches shall be considered as 
protective covering and not included in the effective section. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[10 



Working Stresses 



The stresses for concrete hereinafter given are for concrete composed 
of one part Portland cement and six parts of aggregate capable of develop- 
ing an average compressive strength of 2000 pounds per square inch at 
28 days, when tested in cyhnders 8 inches in diameter and 16 inches long, 
under laboratory conditions of manufacture and storage, using the same 
consistency as used in the field. If the richness is increased, an increase 
may be made in all working stresses proportional to the increase in com- 
pressive strength at 28 days, but this increase shall not exceed 25 per cent. 

Bearing. — When compression is applied to a surface of concrete larger than 
the load area, 650 pounds per square inch may be allowed. 

Axial Compression. — For concentric compression on a plain column or 
pier, the length of which does not exceed 12 diameters, 450 pounds per 
square inch may be allowed. 

Compression in Extreme Fiber. — The extreme fiber stress of a beam 
may be allowed to reach 650 pounds per square inch. Adjacent to the 
support of continuous beams 750 pounds per square inch may be allowed. 



Shear and Diagonal Tension. — When pure shearing stress occurs, 
120 pounds per square inch may be allowed. 

Where the shear is combined with an equal compression, as on a 
section of column at 45 degrees with the axis, the stress may equal one 
half the compressive stress allowed. 

In calculations on beams in which diagonal tension is considered to 
be taken by the concrete, the vertical shearing stresses should not exceed 
40 pounds per square inch. 

Bond. — The bonding stress between concrete and plain reinforcing bars may 
be assumed at 80 pounds per square inch, and in the case of drawn wire 
40 pounds per square inch. 

Reinforcement. — The tensile strength in steel should not exceed 16,000 
pounds per square inch. The compressive stress in reinforcing steel 
should not exceed 16,000 pounds per square inch, or 15 times the working 
compressive stress in the concrete. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[11 



Formulas 



Rectangular beams or unit widths of slabs 



I 



I 




! / 

/ 



•X;/; 



'f^-^" 



I 



:kc 



I 
I 



Fi^.l 



fs 



Standard Notation. 

fg= tensile unit stress in steel 

fc= compressive unit stress in concrete 

N = ratio of modulus of elasticity of steel to modulus of concrete 

M = moment of resistance or bending moment in general 

b = breadth of beam 

d= depth of beam to center of steel 

k= ratio of depth of neutral axis to depth of beam, d 

p = ratio of area of steel to area of concrete 

Position of neutral axis, 



k= i/2 pn + (pn)2 - pn= .38 

Arm of resisting couple, 

j = 1 - % k or %, very approximately 

Fiber stresses, 
f3 = 16,000 
f. = 650 



Steel ratio, 

P=y2. 



a-) 



= .0077 



Area of steel, 

A, = .0077bd 

Moment of resistance, 

M = f3.0077bdx%d 



T-Beams 



Continuous beams reinforced for compression at supports as shown by 

Fig; 2. 
The position of the neutral axis and arm of resisting couple are in practically 
the same location as in rectangular beams. 

Fiber stresses, 

fg =16000 (steel in tension) 

fsi= 11250 (steel in compression) 

fc = 650 (concrete in compression at top of beam) 

fci= 750 (concrete in compression at supports) 

Steel ratio assumed, 
p=.016 



Area of steel, 

A«=.016 bd 



/'whenM = — ^ 



For end spans and spans over two bays only, 

p = .0192 

Area of steel, 

A3 = .0192 bd /^when M=— ^ 
V 10/ 

Moments of resistance, 
M=fg .016 bd X Vs d 
M=f3 .0192 bd X Vs d 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[12 



Formulas 



Beams or unit widths o£ slabs 

Shear, bond and web reinforcement, 

V = total shear 

V = shearing unit stress 

u =bond stress per unit area of bar 
o = circumference or perimeter of bar 
2o = sum of the perimeters of all bars 

In the following formulas ^o refers only to the bars constituting the tension 
reinforcement at the section in question and jd is the lever arm of the 
resisting couple at the section. 

For rectangular beams, 
V 



u 



bjd 
V 



jd.i:o 

(For practical results j may be taken at %.) 

The stresses in web reinforcement may be estimated by means of the follow 
ing formulas: — 

Vertical reinforcement, 

Vs 



f«=- 



jd 



Reinforcement inclined at 45 degrees, 

f» 



Vs 
=0.7 — 

jd 



in which 

fB= stress in single reinforcing member 

V= proportion of total shear assumed as carried by the reinforcement 
and s = horizontal spacing of the reinforcing members 
The same formulas apply to beams reinforced for compression as regards 

shear and bond stress for tensile steel. 

For T-beams, 
V 



v= 



u= 



b'jd 

V 
jd.^o 



(For approximate results j may be taken at %.) 

Columns, 

A = total net area 

Ag = area of longitudinal steel 

Ac= area of concrete 

W = total safe load 

p = ratio of area of steel to area of effective section 

Total safe load, 

W=fe (Ae+nAB) = feA [l + (n -1) p] 

Unit stresses, 
f- P 



A[l + (n-l)p] 



fs = "fc 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[13 



Spacing and Sectional Area of Reinforcement for Slabs One Foot in Width 


STEEL RODS 


WIRE. (W. & M.) 


EXPANDED METAL 


SIZE 


4" 


.205 


5" 
.184 


.167 


6" 


6^' 


7" 


li" 


8" 


8^' 


9" 


9J" 


10" 


lOJ" 


H" 


IW 


12" 


GA. 


SEC. 


2" 


3" 


4" 


MESH. 


GA. 


Designated 


5-16" Ro. 


.230 


.153 


.141 


.131 


.123 


.115 


.108 


.102 


.097 


.092 


.088 


.084 .080 


.077 


No. 


.074 


.443 


.295 


.221 


1-2" 


No. 18 


Stand. 


Sq. 


.292 


.260 


.234 


.213 


.195 


.180 


.167 


.156 


.146 


.137 


.130 


.123 


.117 


.111 


.106 


.102 


.098 


1 


.061 


.368 


.245 


.184 


3-4" 


13 


K 


3-8" Ro. 


.331 


.294 


.265 


.241 


.221 


.204 


.189 


.177 


.166 


.156 


.147 


.139 


.132 


.126 


.120 


.115 


.110 


2 


.054 


.325 


.216 


.162 


1 1-2" 


12 




Sq. 


.422 


.375 


.337 


.307 


.281 


.260 


.241 


.225 


.211 


.198 


.187 


.178 


.169 


.161 


.154 


.147 


.141 


3 


.047 


.280 


.187 


.140 


2" 


12 


CC 


7-16" Ro. 


.451 


.401 


.361 


.328 


.301 


.277 


.258 


.240 


.225 


.212 


.200 


.190 


.180 


.173 


.164 


.156 


.150 


4 


.040 


.239 


.160 


.120 


3" 


16 


It 


Sq. 


.574 


.510 


.459 


.418 


.383 


.353 


.328 


.306 


.287 


.270 


.255 


.241 


.230 


.219 


.209 


.199 


.191 


5 


.033 


.201 


.134 


.101 


3" 


10 


Light 


1-2" Ro. 


.589 


.523 


.471 


.428 


.393 


.362 


.3.36 


.314 


.294 


.277 


.262 


.248 


.236 


.225 


.214 


.204 


.196 


6 


.029 


.174 


.116 


.087 


3" 


10 


Stand. 


Sq. 


.750 


.667 


.600 


.545 


.500 


.462 


.429 


.400 


.375 


.353 


.333 


.316 


.300 


.286 


.273 


.261 


.2.50 


7 


.025 


.148 


.098 


.074 


3" 


10 


Heavy 


9-16" Ro. 


.745 


.663 


.596 


.542 


.497 


.459 


.426 


.398 


.373 


.351 


.331 


.314 


.298 


.284 


.271 


.259 


.248 


8 


.021 


.124 


.083 


.062 


3" 


10 


Ex. Heavj' 


Sq. 


.949 


.844 


.759 


.690 


.632 


.584 


.542 


.506 


.475 


.447 


.422 


.400 


.380 


.362 


.345 


.330 


.316 












3" 


6 


Stand. 


5-8" Ro. 


.920 


.818 


.736 


.669 


.614 


.566 


.526 


.491 


.460 


.433 


.409 


.387 


.368 


.351 


.335 


.320 


.307 












3" 


6 


Heavy 


Sq. 


1.172 


1.042 


.937 


.852 


.781 


.721 


.670 


.625 


.586 


.551 


.521 


.493 


.469 


.446 


.426 


.408 


.391 












4" 


16 


Old Style 


11-16" Ro. 


1.114 


.990 


.891 


.810 


.742 


.685 


.636 


.594 


.557 


.524 


.495 


.469 


.445 


.424 


.405 


.387 


.371 












6" 


4 


Stand. 


Sq. 


1.418 


1.261 


1.134 


1.031 


.945 


.873 


.810 


.756 


.709 


.668 


.630 


.597 


..567 


.540 


.516 


.494 


.473 












6" 


4 


Hea-^y 


3-4" Ro. 


1.325 


1.178 


1.060 


.964 


.884 


.816 


.757 


.707 


.663 


.624 


.589 


.558 


.530 


.506 


.482 


.461 


.442 


















Sq. 


1.687 


1.500 


1.350 


1.227 


1.125 


1.038 


.964 


.900 


.844 


.794 


.750 


.711 


.675 


.642 


.613 1 .606 


.562 



















Ecjuol Secfionql ArcQ of Reinforcement 



^^^■^'■"^-■H- 



.- .--■ .^ _1_1_4-. 



Weights and Areas of Steel Rods 
for Beam Reinforcement 


SIZE 


AREA SQ. 


WT. SQ. 


AREARO. 


WT. RO. 


7-16" 

1-2" 

5-8" 


.191 

.250 

.391 

.562 

.766 

1.000 

1.266 

1..562 


.651 
.850 
1.328 
1.913 
2.603 
3.400 
4.303 
5.312 


.150 
.196 
.307 

.442 
.601 
.785 
.994 
1.227 


.511 
.667 
1.043 
1.502 
2.044 
2.670 
3.379 
4.173 


3-4" 


7-8" 

1" 

1 1-8" 

1 1-4" 


3-16"x3-4" .... 

3-16"xl" 

3-16"xl 1-4".. 


.141 
.187 
.234 


.479 
.637 
.796 







f^s; 



Mirtii'num Lenq+h 
Upper- RooB 

jn-SSpon or 50 Oi£ 






1 ; 1 i ' 



Span, 
b.- 






-i_E£22ii 



V 



-4+- 



-^ |i ^-.\ Ji!.^^j — 



Vtrl-»cal Sfirrups 



■■•Ji; •••■.*' .ir.v' 

.•.•■ll-?.-...Mi.': 
il!..--: • li?. 



-^- 



^■4^:^,^;^v 



2i 



Lap plain rods 2.5 
d lame+ers, deformec 
rods zodlame+cro. 



Fi^. 2 



, , . . . Mmlmum LgnqWi 

Eaual Secrional Area of Ffemforcemenl- , upper Rods' . 
j^ \ fVSSpanorSOOiai 

- f^.^T^'^i:± " - ' — ' ■ ' 



.•^ 



SSvES5S52 






'^ ■ "FT 



Spon. 
-b 



VcrH 



ical Shri-upiJ^' 






^■7^-?-^^i-^- 



-b'- 



Fi^. a 



TYPICAL BEAM REINFORCEMENT 



NOTE. — One lialf of the tension rods may be trussed over supports. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[14 



Number of Rods and Sectional Area 


in Square Inches for Column 


Reinforcement 


SIZE OF ROD 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 


3-4 •■■•sq. 


(1.77 
]2.25 


2.25 


2.65 


3.09 


3.53 


3.98 


4.42 


4.86 


5.30 


5.74 


6.18 


6.63 


7.07 


2.81 


3.38 


3.94 


4.50 


5.06 


5.62 


6.18 


6.75 


7.31 


7.88 


8.44 


9.00 


7-8"....^^- 
sq. 


j 2.41 
t3.06 


3.01 


3.61 


4.21 


4.81 


5.41 


6.01 


6.61 


7.22 


7.82 


8.42 


9.02 


9.62 


3.83 


4.59 


5.36 


6.12 


6.89 


7.65 


8.42 


9.18 


9.95 


10.71 


11.48 


12.24 


j„ dia. 
••••sq. 


f3.14 
14.00 


3.93 


4.71 


5.50 


6.28 


7.07 


7.85 


8.64 


9.42 


9.95 


11.00 


11.78 


12.57 


5.00 


6.00 


7.00 


8.00 


9.00 


10.00 


11.00 


12.00 


13.00 


14.00 


15.00 


16.00 


11^",....^- 


(3.98 
]5.06 


4.97 


5.97 


6.96 


7.96 


8.95 


9.95 


10.94 


11.94 


12.93 


13.93 


14.92 


15.92 


6.32 


7.59 


8.85 


10.12 


11.38 


12.65 


13.91 


15.18 


16.44 


17.71 


18.97 


20.24 


11-4".... 3^- 


f4.91 


6.14 


7.37 


9.60 


9.82 


11.04 


12.27 


13.49 


14.72 


15.95 


17.17 


18.40 


19.63 


\6.85 


7.81 


9.38 


10.94 


12.50 


14.06 


15.63 


17.19 


18.75 


20.31 


21.88 


23.44 


25.00 


1 3-8" . . . .'^'^• 
sq. 


/5.04 
17.56 


7.42 


8.91 


10.30 


11.88 


13.36 


14.85 


16.33 


17.82 


19.30 


20.79 


22.27 


24.76 


9.45 


11.34 


13.23 


15.12 


17.01 


18.90 


20.89 


22.69 


24.58 


26.47 


28.36 


30.25 


, , r,// dia. 
11-2 ■ • ■ sq. 


r7.07 
19.00 


8.84 


10.60 


12.37 


14.14 


15.90 


17.67 


19.44 


21.20 


22.97 


24.74 


26.50 


28.27 


11.25 


13.50 


15.75 


18.00 


20.25 


22.50 


24.75 


27.00 


29.25 


31.50 


33.75 


36.00 



Table for Hooped Column Reinforcement 


DIAMETER OF EN- 


SECTIONAL AREA 


MAXTMTTM PITCH 


LENGTH OF HOOPING 


CLOSED CONCRETE 


HOOPING 




IN 1 FT. IN HEIGHT 


6 inches 


.0187 sq. inches 


IJ inches 


183 inches 


7 " 


.0262 " 




H ' 




178 " 


8 " 


.0350 " 




If ' 




174 " 


9 " 


.0450 " 




2 




171 " 


10 " 


.0500 " 




2 




190 " 


11 


.0619 " 




2i ' 




186 " 


12 " 


.0750 " 




2i ' 




183 " 


13 " 


.0894 " 




2| ' 




180 " 


14 " 


.1050 " 




3 ' 




177 " 


15 " 


.1219 " 




H ' 




175 " 


16 '•' 


.1400 " 




3i ' 




174 " 


17 " 


.1594 " 




31 ' 




172 " 


18 " 


.1800 " 




4 




171 " 


19 " 


.1900 " 




4 




181 " 


20 " 


.2125 " 




4i ' 




179 " 


21 " 


.2362 " 




4i ' 




177 " 


22 " 


.2612 " 




4f ' 




176 " 


23 " 


.2875 " 




5 




175 " 


24 " 


.3150 " 




H ' 




174 " 


25 " 


.3437 " 




5i ' 




173 " 


26 " 


.3737 " 




51 ' 




172 " 


27 " 


.4050 " 




6 




171 " 


28 " 


.4375 " 




6J ' 




170 " 


29 " 


.4712 " 




6^ ' 




170 " 


30 " 


..5062 " 




61 '■ 


169 " 



Material Required for One 
Cu. Yd. Concrete 


Material Required for One Bbl. Cement 


PROPORTIONS OF MIXTURE 


BASED ON 1" STONE 


PROPORTIONS OF MIXTURE 


BASED ON 1" STONE 


CU. FT. 

CONC. 

TO BBL. 

CEMENT 


SIZE OF GAUGE BOXES 


CEM. 


SAND 


STONE 


BBL'S 
CEM. 


CU. YDS. 
SAND 


CU. YDS. 
STONE 


CEM. 


SAND 


STONE 


BBL'S 

CEM. 


CU. YDS. 
SAND 


CU. YDS. 
STONE 


SAND 


STONE 


1 
1 
1 

1 


1 1-2 
2 

2 1-2 
3 


3 
4 
5 
6 


1.99 
1.58 
1.29 
1.11 


0.42 
0.44 
0.46 
0.47 


0.84 
0.89 
0.91 
0.94 


1 
1 

1 
1 


1 1-2 
2 

2 1-2 
3 


3 
4 
5 
6 


1 
1 

1 
1 


0.21 
0.28 
0.35 
0.42 


0.42 
0.56 
0.70 
0.84 


13 1-2 

17 

21 
24 1-3 


3'x6'x3 3-4" 
3'x6'x5 1-16" 
3'x6'x6 5-16" 
3'x6'x7 1-2" 


3'x6'x 7 1-2" 
3'x6'xl0 1-8" 
3'x6'xl2 .5-8" 
3'x6'xl5" 



Notes. — One bag cement weighing .95 lbs. = .95 cu. ft. in volume. Four bags cement = 3.8 cu. ft. = 1 bbl. 
For footings, heavy foundation walls, heavy machine foundations and similar work use 1-3-6 mix. 
For piers, light foundation walls, light machine foundations and similar work use 1-2^-5 mix. 
For reinforced concrete girders, beams, slabs, and thin walls use 1-2-4 mix. 
For reinforced concrete columns use l-li-3 mix. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[15 



Design of Slabs 



Directions for usin^ Chart No. 1.* — Determine load to be carried, 
and span in feet. Follow vertically frona span at bottom of chart for 
M=wl^ -T- 10, or from top of chart for M = wP -;- 12, to curved line repre- 
senting bending moment in foot-pounds due to load assumed, thence hori- 
zontally to columns at left of chart, where thickness of slab, and sectional 
area of steel per foot in width of slab, will be found. From sectional area 
of steel determine the spacing of rods of type of fabricated metal from the 
table showing "spacing and sectional area of reinforcement for slabs 
1 foot in width." 

Example. —Assume combined live and dead loads at 250 pounds per square 
foot. Assume span of 10 feet over three or more spans, which would 
allow wP -7- 12 to be used. Follow vertically downward from figure 10 
to line marked "250 pounds per square foot, M=wP-h12," thence 
horizontally to right, where it is found that a 5i-inch slab Avith .40 square 
inch of steel per foot in width of slab is required; or a 6-inch slab with 



.36 square inch of steel; or a 65-inch slab with .325 square inch of 
steel, etc. 

As the largest area of steel shown by the chart gives the most economi- 
cal combination, the 5^inch slab with .40 square inch of steel should be 
adopted. 

To determine spacing of rods consult table for spacing, and there it 
will be found that %6-inch round rods, 4J inches on centers, or ^-inch 
round rods, 6 inches on centers, or ^inch square rods, 7^ inches on centers, 
or various other sizes or spacings can be used for the .40 square inch 
per foot in width. ~ 

It also shows that a 3-inch No. 6 Standard Expanded Metal gives the 
requisite sectional area of steel. 



Weight of Concrete Slabs per sq. £t. 

Thickness; inches 3 3i 4 4J 5 5^ 6 6^ 7 7i 8 

Weight; pounds 37 44 50 56 62 69 75 81 87 94 100 



♦Chart No. I is to be used for detenniiiing tbickness of and amount of reinforcement required in 
concrete slabs for any load and span within limits given. 



CHART NO. I 

REINFORCED CONCRETE SLABS 



GQ 
< 

H) 

u 

O 

X 
h 
Q 

Z 

h 
o 
o 
u. 

a 

Ul 

a 

(J 

Z 

lU 


GC 

2 

z 

UJ 

a: 

(1. 



< 

Ul 

a 
4 

J 
< 

z 



h 


LU 
<0 


THICKNESS OF SLAB IN INCHES. 


Ma 

IN 
P T LBS 

7,000 
6750 
6500 
6250 
feOOO 
5750 
5500 
5250 
5000 
4750 
4500 
4250 
4000 
3750 
3500 
3250 
3000 
2750 
2500, 
2250 
2000 
1750 
1500 
1250 
1000 
750' 
500 
250 


BENDING MOMENT FOR UNIFORMLY DI5TRIBUTED LOADS. 


3 


3i 


A^ 


^t 


5 


51 


6 


6i 


7 


7t 


8 


SPAN IN FEET. ^ Ma = v^/p ^ IZ CONTINUOUS SPAMS 

Ife 15 14- 13 (Z II lO 9 a 7 6 5 4 3 ^- 1 




























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\ 


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/ 




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\i< 






IT 


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\^ 


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w 


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/ 


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SPAN IN FEET. ' Mb = wl^-HlO END SPANS 


\h 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[17 



Design of T-Beams 



Directions for usin^ Charts Nos.IIA and II B.* — Determine load 
to be carried per lineal foot of beam, and span in feet. Follow vertically from 
span assumed on chart II A for M=wP h-10, or on II B for M = wP -^ 
12 to straight Une giving shear due to load assmned, thence to right, where 
will be found the "Effective Web Area" required, also sectional area of 
vertical steel in a length equal to the effective depth (i.e., the distance 
between the center of compression in the concrete and the center of tension 
in steel = | d.) 

After determining effective web area, return to span at bottom of chart, 
and follow vertically to curved line representing bending moment due to 
load assumed, thence to left to column where effective web area does not 
exceed the area previously determined. 

From this column take the depth of beam, the width of stem 
being found at the top of the coliunn. Opposite the depth in column 
marked "S" will be found the requisite sectional area of steel throughout 
bottom of beam, and over supports, for the distance shown in cut. 



Example. — Assume combined live and dead load of 2400 pounds per lineal 
foot. Assume span of 20 feet. For intermediate spans use chart II B. 
Follow vertically from figure 20 at top of this chart to straight Hne marked 
"2400 pounds per lineal foot, " thence to right, where it is found that an 
effective web area of 200 square inches and a sectional area of vertical steel 
of 1 square inch are required. Then from figure 20 at bottom of chart follow 
vertically to curved line marked "2400 pounds per hneal foot" MB = wF 
-i- 12, thence to left, where it is found that a beam 12 inches x 21 J inches with 
4.38 square inches steel is required. An equal area of steel is to be used 
at center of span and over supports. 



The effective depth of this beam is f (21 J inches — 2i inches) = 19 
inches. 

The 4.38 square inches of tension steel can be made up by using two 
J-inch and one l|-inch square rods with a combined sectional area of 4.39 
square inches. 

If %6-inch X 1-inch stirrups are used with a sectional area of .187 
square inch for each of a pair of upright prongs, then the spacing of the 
stirrups for maximum shear would be 
.187x2 



100 



X 19=7.1 inches. 



The stirrups are to be continued with spacing in proportion to intensity 
of shear to a point where shear is not over 40 pounds per square inch in 
effective web area. 

For end spans use chart II A in a similar manner. 

Cuts Nos. 2 and 3 show a method of complying with the require- 
ments. 

Rectangular Beams. — Where it is necessary to use a beam of rectangular 
section, the sectional area of steel in tension should not exceed .77 of 1 per 
cent of the area of the concrete above the center of the steel. 
Let fg = unit stress in steel, or 16,000 

d = distance between top of slab and center of steel in inches 
b = breadth of beam in inches 
Then Moment of Resistance in foot-pounds, where .77 of 1 per cent 
of steel is used 



= 1 



(.0077 i, X bd^) 
12 



=9 bd^, approximately. 



If less steel is used, the Moment of Resistance will be in direct pro- 
portion to the amount of steel. 



♦Charts Nos. II A and II B are to be used for determining the dimensions of and the amoimt of 
reinforcement required in concrete T-beams for any load and any span within Umits given. 



CHART NO. II A 

REINFORCED CONCRETE T-BEAMS 

NOTE. — Use for end spans, and spans over one or two bays 



DIMENSIONS OF T-BEAMS 


Mb 

INTHOUS 
FT LBS 


MAXIMUM BENDING MOMENT AND SHEAR FOR UNIFORMLY DISTRIBUTED L0i\D5. 




U < 

LU ID 
U-tLl 


a. £ 

lu 


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tWlDE 


lO'WlDE 


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lil^'NA/IDE 


SPAN IN FEET USE FOR SHEAR 

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3tPTI1 


WCB 


STCTl 


DtPTM 


AREA 


AUtA 

srta 


DEfTH 


WEB. 
ABE/k 


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DEPTh 


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sTtn 


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AREA 


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DEPTH 


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IN 


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35 


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427 


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350 

340 

330 

320 

310 

300 

290 

280 

2 70 

260 

250 

240 

230 

2 20 

2 10 

200 

190 

180 

170 

160 

150 

140 

130 

120 

1 10 

100 

90 

80 

70 

60 

50 

40 

30 

20 

10 


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70 
68 
66 
64 
62 
60 
58 
56 
54 
52 
50 
48 
46 
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583 

567 

550 

533 

517 

500 

483 

467 

450 

433 

417 

400 

383 

367 

350 

333 

3r7 

300 

283 

267 

250 

Z33 

217 

200 

183 

167 

ISO 

133 

117 

100 

83 

67 

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17 


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275 
2.67 
258 
2^0 
242 

2.25 
2.17 
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31 30 29 28 27 26 25 '24 23 ZZ 21 20 13 18 17 I& 15 14 13 12 II 10 3 8 7 6 5 4 3 2 1 
SPAN IN FEET USE FOR Mb = ^ 





NOTE. — *Flange of beam must be at least 4 
at least % inches thick. HFlange of beam must 



inches thick. fFlange of beam must be at least 4i inches thick. JFlange of beam must be at least 5 inches thick. §Fiange of beam must 
be at least 6 inches thick. **Flange of beam must be at least 6i inches thick. 



be 



CHART NO. II B 

REINFORCED CONCRETE T-BEAMS 

NOTE. — Use for continuous spans over three or more bays. 



DIMENSIONS OF T-BEAM5. 


Mb 

mTHOus 


MAVIMUM BENDING MOMENT AND SHEAR FOR UNIFORMLY DISTRIBUTED LOADS. 




> ut 


I? 

tf) til 

c 


— s'vv.tid 


-7"-VVl OE 


8" VVIOE 


irt"svioe 


l2-W,o£ 


15" vVipe 


SPA.N IM FEET v/ USE FOR SMEAR. 
1 Z 3 4. 5 6 7 8 3 10 11 12 (3 14 15 I& 17 Ift 15 EO ai 22 23 24 25 26 27 Z8 29 30 31 


OESTIt 


AREA ;nii 


OEPTM 


WEB 

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AREA 
JTCEt 


DEPTH 


WE6 
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AREA 
5TEEI 


BtlTX 


WEB 

AHEA 


ARCA 

srra 


DEITX 


WEB 
AREA 


AREA 
STEEl 


lEPTH 


WEB 

A«rA 


ABEfl 
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FT LBS 


IN. 


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350 
340 
330 
320 
310 
300 
290 
280 
270 
260 
250 
2^0 
230 
Z20 
210 
200 
190 
180 
170 
IfeO 
150 
140 

tao 

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1 (O 

too 

90 
80 
70 
60 
50 
4.0 
30 
20 
10 


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70 
68 
G6 
64 
62 
60 
58 
Sfo 
54 
52 
50 

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583 
567 
550 
533 
517 
500 
433 
467 
450 
433 
4(7 
400 
383 
367 
350 
333 
317 
300 
283 
267 
250 
233 
217 
200 
183 
167 
150 
133 
117 
100 
83 
67 
50 
33 
17 


E3Z 
233 
2.75 
2.67 
258 
250 
242 
233 
2.25 
217 
208 
200 
1.92 
1.83 
1.75 
1.67 
1.58 
1.50 
I4Z 
1.33 
1.25 
1.17 
1.08 
1.00 

m 

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31 30 Z') 28 27 26 25 24 25 22 21 20 19 18 >7 16 15 14 13 IZ II lO 9 ^ft 7 fe S ^ 3 2. 1 
SP/^N IN FEET USE FOR Ms = "f^ 





NOTE. — *Flange of beam must be at least 4 inches thick. tFlange of beam must be at least 4§ inches thick, JFlange of beam must be at least 5 inches thick. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[20 



Design o£ Columns 



Directions for usin^ Chart No. III.* — Determine load to be carried, 
determine mixture of concrete, percentage of steel and type of column to 
be used. Follow vertically from load at bottom of chart to curves for 
1:2:4 concrete, or from load at top of chart to curves for 1:1^:3 concrete, 
thence horizontally to right, where dimensions of column and amount of 
reinforcement are given. 

Example. — Assume load of 400,000 pounds to be carried on a column com- 
posed of 1 : 2 : 4 concrete with 3 per cent longitudinal steel. Follow vertically^ 
from figure 400 at bottom of chart to curve marked "1:2:4 concrete, 3 per 
cent steel," thence to right to columns marked "A," where it is found that 
a column 25 inches square, 28J inches diameter or 27J inches octagonal, 
reinforced with about 18.75 square inches steel is required. Add 3 inches 
to side or diameter of column to allow for protective covering. 

Or assume this load to be carried on a hooped column composed of 
1:1J:3 concrete vsdth 3 per cent vertical reinforcement. Follow vertically 
from figure 400 at top of chart to curve marked "1 : 1^: 3 concrete, 3 per 
cent steel," thence to right to columns marked "C," where it is found 



that a column 21 J inches diameter reinforced with 10.5 square inches steel 
is required. 

By referring to table for number and size of rods corresponding to 
sectional area, it is found that 18.75 square inches will require twelve IJ- 
inch square rods, and 10.5 square inches will require six l^inch diameter 
rods; or such other combinations can be made as are desu'able. 

By referring to tables for amount of hooped reinforcement, the size 
and spacing of hooping is found. 

Hooped Reinforcement. — Based on 1 per cent of volume of enclosed 
concrete. 
Let D = diameter of enclosed concrete 

Aii= sectional area of one strand of hooping for maximum pitch 

P = maximum pitch allowable 

h = length of hooping in 1 foot in height of column 

Formulas:— Ai,= .0025 PD; h=.38 D ^ P. 

If rods of sectional area less than A^ are used, then the pitch may be 
decreased in direct ratio, and the length h increased in inverse ratio. 



♦Chart No. Ill is to be used for determining the dimensions of, and the amount of reinforcement 
required in, concrete columns of different designs and shapes as shown, for any load within 
limits given. 



CHART NO. Ill 
PLAIN AND REINFORCED CONCRETE COLUMNS 




40 60 80 100 120 140 160 180 200 220 240 2fcO Z80 300 320 340 3fc0 380 400 4Z0 440 460 4S0 500 520 540 560 580 600 



THOUSANDS OF POUtSPS FOR 1:2:4 CONCRETE 



NOTE. — "A" refers to columns without hooping, "B" to columns without longitudinal reinforcement, and "C" to hooped columns with vertical reinforcement. 



DESIGNERS' CHARTS FOR REINFORCED CONCRETE 



[22 



Cost of Materials 



Directions for usin^ Chart No. IV. — The chart gives the cost of 
concrete of the various mixtures shown when unit prices of materials 
are known. 

The four upper Hues give the cost per cubic yard, the intermediate 
line the cost per 100 square feet of granolithic surface 1 inch thick, and 
the lower lines the cost of 10 square feet of slabs or walls of concrete up 
to 12 inches in thickness. 

The upper line of figures at the bottom of the chart indicates the 
cost per cubic yard of stone, sand or per barrel of cement. 

The lower line represents the cost per ton of stone or sand corre- 
sponding to the yard price, based upon the assumption that a yard of stone 
or sand weighs 2700 pounds. 

The table gives the quantities of material required by the various 
proportions of mixtures and sizes of gauge boxes to measure them. 

Examples. — Examples showing use of chart. To determine cost of materials 
in 1 cubic yard 1:2:4 concrete, assuming the cost of stone as fl.40 per 
ton; sand $1.20 per yard; and cement $1.45 per barrel: — 

Cost of stone. Follow vertically from 1.40 in lower space to line 
designated "cost per cubic yard 1 : 2 : 4 concrete, " thence horizontally to 



first column at right, where it is found that $1.64 is the cost of the 
stone. 

Cost of sand. Follow vertically from 1.20 in upper space to same 
line, thence to second column at right, where it is foimd that $0.53 is the 
cost of the sand. 

Cost of cement. Follow vertically from halfway between 1.40 and 
1.50 in upper space to same line, thence to right to fifth column, desig- 
nated "cost of cement 1:2:4," where it is found that $2.39 is the cost of 
the cement. 

Total cost of material for one yard of 1:2:4 concrete: — stone 
$1.64, sand $0.53, cement $2.30, total $4.47. 

To determine cost of materials in 100 square feet of 1 inch grano- 
lithic surface: — 

Assume unit price on stone, sand and cement the same as before. 
Start from same figures as before and follow vertically to line representing 
cost of granolithic surface, thence to first, second and last columns, where 
it is found that the stone costs $0.82, the sand $0.27 and the cement $1.95, 
making a total cost for materials for the 100 square feet of $3.04. 

To determine the cost of 10 square feet of slab or wall of any thickness 
up to 12 inches apply the same methods as described in the preceding cases^ 



CHART NO. IV 

COST OF CONCRETE MATERIALS (not including labor) 




^ 



4 
J 



1 



"^ 



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